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Catastrophes in quantum many-particle systems

Caustics are a dramatic wave focusing phenomenon well known in optics (rainbows, bright lines on the bottom of swimming pools) and hydrodynamics (ships wakes, tsunamis). Starting in the 1970s it was realized that there is a rich mathematical structure underlying caustics described by catastrophe theory which shows that certain shapes of caustic are stable against perturbations and hence occur generically in nature. As quantum mechanics is described by a wave equation it is natural to ask whether caustics can occur in quantum systems too?

The answer is yes and the single-particle case is essentially the same as (classical) optics. I will therefore focus on the more interesting case of many-particle quantum systems where a new class of caustic can occur: a quantum catastrophe. I will give various examples including ``light cones’’ in spin chains following a quench, Bose-Einstein condensates in double and triple wells (or equivalently spin-1/2 and spin-1 BECs), and Hawking radiation.